# Some Properties of Edge-intersection Graph of 3-uniform Hypergraphs of Order 6n and Size 4n

## Abstract

Let  $\dpi{100}&space;H=(V,E)$ be a $3$-uniform, $2$-regular, connected hypergraph of order $6n$ and size $4n$ for some $n&space;\in&space;\mathbb{N}$. For $e&space;\in&space;E$, let $E_e=\{f\in&space;E&space;\backslash\{e\}:e\cap&space;f\neq\O\}$, the transversal number of a hypergraph $H$ in which $|E_e|=2$ for all $e\in&space;E$ are investigated. In this paper, we interested in studying some properties of an edge-intersection graph $L(H)$ of a hypergraph $H$ such as the vertex cover, the matching, and the independent set. We prove that  $L(H)$ is a bipartite graph and the transversal number of $H$ is equal to the vertex covering number of $L(H)$.

Section
บทความวิจัย

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